High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the type of periodic signal employed. The paper uses the method of averaging as well as numerical integration to study a single-degree-of-freedom (SDOF) system consisting of a mass in frictional contact with a translating surface. Recently, it was found that sinusoidal dither forces had the ability to stabilize or destabilize such a system, depending on the system and frictional characteristics as well as the amplitude and frequency of the dither signal [1]. This paper extends this analysis to general, periodic dither forces. In particular, the system response for sinusoidal dither waveforms is compared to that of triangular dither waveforms and square dither waveforms. It is found that, for a given amplitude and frequency of the dither signal, square waveforms are much more effective in canceling friction-induced oscillations than sinusoidal dither; likewise, sinusoidal waveforms are more effective than triangular waveforms for a given amplitude and frequency. A criterion is developed that relates the effectiveness of the waveform to the properties of the integral of the dither signal.
Experimental study of a passive inverted pendulum control system
